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127 LearnersLast updated on December 11, 2025
Lateral Surface Area of a Trapezium
A trapezium is a quadrilateral with one pair of parallel sides, known as bases, and the other pair being non-parallel sides. The lateral surface area pertains to the sum of the areas of the non-parallel sides, often called lateral sides. Let's consider a tent with a flat top; the sloping sides represent the lateral surface area of the trapezium formed by the tent.
What is the Lateral Surface Area of a Trapezium?
The lateral surface area of a trapezium refers to the area covered by the non-parallel sides of the trapezium.
Formula for Lateral Surface Area of a Trapezium
To find the lateral surface area of a trapezium, we sum the lengths of the non-parallel sides.
If 'a' and 'b' are the lengths of the non-parallel sides, the lateral surface area (LSA) is simply a + b.
How to Find Lateral Surface Area of a Trapezium
To determine the Lateral Surface Area of a Trapezium, follow these steps:
Step 1: Identify the lengths of the non-parallel sides.
Step 2: Ensure all measurements are in the same unit before proceeding with the calculation.
Step 3: Use the formula LSA = a + b, where a and b are the lengths of the non-parallel sides.
Step 4: Present the calculated result in linear units.
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Common Mistakes and How to Avoid Them in the Lateral Surface Area of a Trapezium
There are a few typical mistakes people make while calculating the lateral surface area of a trapezium.
Some of them are listed below:
Mistake 1
Confusing the bases with the lateral sides.
It's a common mistake to confuse the parallel bases with the lateral sides.
Remember, the lateral surface area only involves the non-parallel sides.
Mistake 2
Incorrect addition of side lengths.
Ensure that the correct sides are being added when calculating the lateral surface area.
Double-check the measurements before finalizing the answer.
Mistake 3
Not mentioning the units with the numerical value.
It's important to mention the unit with the answer, even if the question doesn't specify it.
It's preferable to use the standard linear units.
Mistake 4
Rounding in earlier steps.
Even though rounding may be necessary, doing it too early can lead to inaccuracies.
Round off the final answer only if needed.
Mistake 5
Confusing lateral surface area with total surface area.
Lateral surface area refers to the sum of the non-parallel sides, while total surface area would include all sides of the trapezium.
Solved Examples on Lateral Surface Area of a Trapezium
Problem 1
What is the lateral surface area of a trapezium with non-parallel sides measuring 5 cm and 7 cm?
12 cm
Explanation
Given: Non-parallel side a = 5 cm, Non-parallel side b = 7 cm
LSA = a + b = 5 + 7 = 12 cm
Problem 2
If a trapezium has non-parallel sides of lengths p cm and 10 cm, and their sum is 25 cm, find the value of p.
15 cm
Explanation
Given: Non-parallel side a = p cm, Non-parallel side b = 10 cm
LSA = a + b = 25 cm
Solving for p: p + 10 = 25
p = 25 - 10
p = 15 cm
Problem 3
Calculate the lateral surface area of a trapezium where the non-parallel sides are 8 cm and 3 cm.
11 cm
Explanation
Given: Non-parallel side a = 8 cm, Non-parallel side b = 3 cm
LSA = a + b = 8 + 3 = 11 cm
Problem 4
Evaluate the length of one non-parallel side if the other is 9 units and their combined length is 20 units.
11 units
Explanation
Given: Non-parallel side a = 9 units Combined length = 20 units
Let the other side be b: a + b = 20
9 + b = 20
b = 20 - 9
b = 11 units
Problem 5
The non-parallel sides of a trapezium measure 12 cm and 5 cm. What is the lateral surface area?
17 cm
Explanation
Given: Non-parallel side a = 12 cm Non-parallel side b = 5 cm
LSA = a + b = 12 + 5 = 17 cm
FAQโs on Lateral Surface Area
1.What is Lateral Surface Area?
2.How to calculate the lateral surface area?
3.Is the lateral surface area and the perimeter the same?
4.What distinguishes lateral sides from bases?
5.How does changing the non-parallel side lengths affect the LSA?
Important Glossary for Lateral Surface Area
- Trapezium: A quadrilateral with one pair of parallel sides.
- Lateral sides: The non-parallel sides of a trapezium.
- Bases: The parallel sides of a trapezium.
- Linear units: Units used to measure length, such as centimeters or meters.
- Sum: The result of adding two or more numbers or quantities.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
